Signed Formulae as a New Update Process

Introduction

The agent paradigm has recently increased its influence in the research and development of computational logic-based systems. A clear and correct specification is made through Logic Programming (LP) and Non-nomotonic Reasoning that have been brought (back) to the spot-light. Also, the recent significant improvements in the efficiency of LP implementations for Non-monotonic Reasoning (De Schreye, Hermenegildo & Pereira, 1999) have helped to this resurgence. However, the agents need update constantly their knowledge base and, particularly the intentional base (rules) such that our agent has the ability to reacting to changes in dynamic environments is of crucial importance within the context of software agents. Such feature should correspond to a deliberative rational behavior wanted for our agents.

The quality of the service that an agent offers is based on the form in which an agent combines rationality and reactivity. A reactive agent can offer well evaluated recommendations but, this response is based on outdated information, while a rational behavior may generate recommendations based on the most recently acquired information. So, we are interested in developing environment-aware agents. For this reason, is very important to have an update process for agents, i.e., that it allows us to design agents with its rational component.

Over recent years, several semantics for logic program updates have been proposed (Brewka, Dix, & Knonolige 1997) (De Schreye, Hermenegildo, & Pereira, 1999) (Katsumo & Mendelzon, 1991). All these semantic ones coincide in considering the AGM proposal as the standard model in the update theory, for their wealth in properties. The AGM approach, introduced in (Alchourron, Gardenfors & Makinson, 1985) is the dominating paradigm in the area, but in the context of monotonic logic. All these proposals analyze and reinterpret the AGM postulates under the Answer Set Programming (ASP) such as (Eiter, Fink, Sabattini & Thompits, 2000). However, the majority of the adapted AGM and update postulates are violated by update programs, as shown in (De Schreye, Hermenegildo, & Pereira, 1999). For this reason, we have been working in finding properties that our update operator satisfies (Osorio & Zacarías, 2003) (Zacarías & Osorio, 2005) (Arrazola & Zacarias, 2005). Our purpose is to build a semantics based on structural properties. This is our main objective in the update theory. In (De Schreye, Hermenegildo, & Pereira, 1999) (Osorio & Zacarias, 2003) (Zacarías, Osorio & Arrazola, 2005) (Zacarias, 2005) the authors present a set of properties that the update operator satisfies. In this paper we continue with this same research line presenting a novel proposal with the aim to enrich the update theory that we have begun in (Osorio & Zacarias, 2003) (Zacarías, Osorio & Arrazola, 2005) (Zacarias, 2005). This novel proposal contributes with two benefits. First, we conserve many of the properties presented in previous works (Osorio & Zacarias, 2003) (Zacarías, Osorio & Arrazola, 2005) (Zacarias, 2005), such as: Weak Irrelevance of Syntax (WIS). This property is similar to one postulate proposed by AGM, but in this case for nonmonotonic logic and under Answer Set Programming (ASP) introduced and defined by (Gelfond & Lifschitz, 1988).